Solutions and perturbation estimates for the matrix equation \(X^s+A^*X^{-t}A=Q\)

DOI10.1016/j.laa.2009.05.010zbMath1179.15015OpenAlexW2104438552MaRDI QIDQ840638

Liang Fang, San-Yang Liu, Xiao-Yan Yin

Publication date: 14 September 2009

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2009.05.010

zbMATH Keywords

numerical examplesiterative methodnonlinear matrix equationHermitian positive definite matrixperturbation estimate

Mathematics Subject Classification ID

Related Items (11)

On the perturbation estimates of the maximal solution for the matrix equation \(X + A^T \sqrt{X^{- 1}} A = P\) ⋮ Unnamed Item ⋮ Some investigation on Hermitian positive-definite solutions of a nonlinear matrix equation ⋮ Positive definite solutions of the matrix equations ⋮ Solutions and perturbation analysis for the nonlinear matrix equation \(X + \sum^m_{i=1} A^*_i X^{-1} A_i = I\) ⋮ Positive definite solutions and perturbation analysis of a class of nonlinear matrix equations ⋮ Positive definite solutions of the nonlinear matrix equation \(X+A^*X^qA=Q\) (\(q>0\)). ⋮ Solutions and improved perturbation analysis for the matrix equation \(X-A^\ast X^{-p}A=Q(p>0)\) ⋮ Unnamed Item ⋮ On Hermitian positive definite solutions of a nonlinear matrix equation ⋮ Perturbation analysis of the nonlinear matrix equation \(X - \sum_{i = 1}^m A_i^* X^{p i} A_i = Q\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On two perturbation estimates of the extreme solutions to the equations \(X \pm A^*X^{-1}A = Q\)
• Iterative methods for the extremal positive definite solution of the matrix equation \(X+A^{*}X^{-\alpha}A=Q\)
• On the existence of a positive definite solution of the matrix equation \(X+A^ T X^{-1} A=I\)
• On the positive definite solutions of the matrix equations \(X^{s}\pm A^{\text T} X^{-t} A=I_{n}\)
• On Hermitian positive definite solutions of matrix equation \(X+A^{\ast} X^{-2} A=I\).
• On the nonlinear matrix equation \(X+A^*{\mathcal F}(X)A=Q\): solutions and perturbation theory
• Perturbation analysis for solutions of \(X \pm A^{\ast}X^{-n} A = Q\)
• On positive definite solutions of the nonlinear matrix equation \(X+A^* X^{-n} A=I\)
• Perturbation analysis of the maximal solution of the matrix equation \(X+A^*X^{-1}A=P\). II
• Solutions and perturbation estimates for the matrix equations \(X\pm A^*X^{-n}A=Q\)
• The iterative method for solving nonlinear matrix equation \(X^{s} + A^{*}X^{-t}A = Q\)
• On positive definite solutions of the family of matrix equations \(X+A^*X^{-n}A=Q\).
• On positive definite solution of a nonlinear matrix equation
• Positive Definite Solutions of Operator Equations X m + A * X − n A = I
• Improved methods and starting values to solve the matrix equations $X\pm A^*X^{-1}A=I$ iteratively
• Computing the Extremal Positive Definite Solutions of a Matrix Equation

This page was built for publication: Solutions and perturbation estimates for the matrix equation \(X^s+A^*X^{-t}A=Q\)